Japan has extreme gun control, and they have a higher rate of suicide than the U.S. Instead of guns, they use subways, knives and cars to kill themselves. The tool used is irrelevant.
To be fair that isn’t exactly apples to apples, as there isn’t traditionally so strong a taboo against suicide in Japanese culture. Not that there’s any country that promotes suicide, exactly, given the strong natural human resistance to death. Maybe the old Soviet Union had a culture of death, though half on purpose and half not.